The invention disclosed herein relates generally to the field of securities whose value is based on future cashflows, and analysis thereof, including providing valuations thereof. One example of such a security is mortgage-backed securities (MBSs). Other securities (or derivatives, instruments, etc.) to which the disclosure herein applies are those whose value is interest path dependent. The invention relates to methods, systems and computer program products for implementing such valuation and analysis.
MBS instruments, which comprise pools of mortgages and collateralized mortgage obligations (CMOs), are analyzed for various reasons including computing valuations and metrics such as pricing, effective duration and key rate durations, and sensitivity to market variables. MBS instrument valuations and metrics may be provided for different interest rate models and for different market scenarios within an interest rate model. An interest rate model “predicts” what the interest rates will be in the future over a specified period of time based on model assumptions and/or parameters obtained from past market behavior. Since future interest rates are uncertain, a credible interest rate model offers many different possible “paths” for future interest rate dynamics. For example, an “exogenous” interest rate model uses the current yield curve as a starting point in its “prediction” of future interest rates. One interest rate model currently in use assumes normal dynamics of instantaneous “short” rate driven by two stochastic factors (so-called two factor Hull-White model). The specific dynamics are defined by the following parameters: current yield curve; ATM (at-the-money) swaption implied volatilities for 2-year and 10-year tenors for different maturities; mean reversion of each of the 2 stochastic factors (assumed constant); and correlation between the factors.
MBS analytics strive to answer various questions about the behavior of an instrument based on the change in the market. MBS valuations involve interest rate path simulations and cashflow computations. MBS instruments may have many possible interest rate paths along which cashflows may be generated dependent on interest rates, prepayments, defaults, and other market variables in general. Interest rate paths, which each can comprise a series of future interest rates on a specified schedule based on an interest rate model, can be simulated based on current interest rate term structure and ATM volatilities (A simulated interest rate path (or paths) is referred to herein as an “interest rate path” (or “paths”)). Cashflow paths are computed based on structure of MBS, interest rate paths, prepayment and default assumptions, and other conditions.
Methodologies for computing such valuations and metrics, and for simulating interest rate paths and for computing cashflows are known in the art, and are discussed, for example, in: Analysis of Mortgage Backed Securities, Harvey J. Stein, Alexander Belikoff, Kirill Levin and Xusheng Tian, Jan. 5, 2007 & Sep. 3, 2008; Mortgage OAS Analysis, Harvey Stein, Feb. 16, 2006; A Theoretical and Numerical Analysis of Collateralized Mortgage Obligations, Bjornar Andre Ulstein, Master Thesis in Financial Economics, The Norwegian School of Economics and Business Administration, Jun. 18, 2008; Fixed-Income Securities and Derivatives Handbook, Moorad Choudhry, Bloomberg Press, Princeton, N.J., 2005; and Cash Flow Models for Pricing Mortgages, Philip Booth and Duncan Walsh, Research Paper 2000.02, City University Business School, London, November 2000, the entire disclosures of all of which are incorporated herein by reference.
Generally, the price, or present value, of an MBS instrument is the average of its discounted cashflows along each simulated cashflow path and along each simulated interest rate path. For example, see Expression 1 below. (The Expressions referred to herein may be found in the mathematical presentation below.) A discount factor is the present value of a unit of currency due to be paid at the end of a given period.
Pricing of MBS instruments involves non-linear analyses, and typically includes the use of Monte Carlo simulations, e.g., computational algorithms that rely on repeated random sampling to compute their results, which involve significant complexity, computer processing and computer storage resources. This makes such simulations very expensive for on-demand use, even when used with variance reduction techniques.
Because of complexity, cost and resource requirements, MBS valuations typically include two stages of processing performed at different times. In a first stage of processing (Stage 1), a number of interest rate paths are simulated and cashflow paths, e.g., a sequence of future payments made by the MBS instrument on a specified schedule, are computed for each interest rate path.
In Stage 1 processing in this previous approach, for a particular interest rate model, all of the interest rate paths are generated (and stored), and used to compute the cashflow paths along each of the interest rate paths for each market scenario in the valuation. In addition, Stage 1 processing also computes the discount factors for each cashflow path. This processing is performed once for a concerned instrument or set of instruments and saved for use in Stage 2 processing. Since Stage 1 processing typically involves large numbers of interest rate paths and cashflow path computations, which consumes significant computer processing and storage resources, such processing is typically run on a scheduled basis, e.g., nightly, as opposed to on-demand, e.g., when an investor requests a price for an instrument.
In a second stage of processing (Stage 2), pricing is computed using the previously computed cashflow paths and discount factors, and the current market environment for the particular instrument, i.e., observable market “parameters” at a given time which may vary in time and which are not specific to any instrument being analyzed. For example, these parameters may include the interest rate model parameters discussed above.
Stage 2 processing is performed on demand typically hours after or the day after Stage 1 processing. This allows very fast on-demand calculation of the MBS price based on the current market environment and the interest rate paths and cashflow paths previously calculated in Stage 1 processing, while reflecting changes in the market environment since the Stage 1 processing.
However, while Stage 1 processing and Stage 2 processing both are based on the then current market environment, since the processing takes place at different times or on different days, the market environments on which the Stage 1 and Stage 2 processing are based are typically different. For example, Stage 1 processing is performed overnight based on the previous day's market environment and Stage 2 processing is performed on demand the next day based on the current day's market environment. Therefore, pricing of MBS instruments using this previous approach may not accurately reflect the market environment at the time of the on-demand Stage 2 processing.
Also, while the current two stage approach may be suitable for less complex valuations, e.g., involving lower numbers of market scenarios and interest rate paths, because of complexity and required resources, the current two stage approach may not be scalable for more complex valuations involving larger numbers of market scenarios. For example, the current two stage approach may be suitable with respect to processing and storage resources and timeliness for a valuation including, e.g., three market scenarios (the current market environment; parallel shift up from the current market environment; and parallel shift down from the current market environment) and 32 interest rate paths (which requires 96 cashflow path computations). However, the current two stage approach may not be suitable from a quantitative standpoint for more complex MBS valuations involving larger numbers of scenarios and/or interest rate paths because of the increased processing and storage requirements.
Additionally, different investors may have differing views as to what variables most appropriately represent the market environment, and may want price, option adjusted spread (OAS), effective duration, key rate durations and other metrics computed for an MBS instrument in such a manner that the investor can specify the market environment. For example, the investor may desire to choose a specific type and date of a yield curve, may provide a custom curve, or may change the inputs for the analysis (price or OAS). However, the current two stage processing approach does not easily accommodate user-selected variables and metrics.